CN115551013A

CN115551013A - Unmanned aerial vehicle deployment and task unloading method in multi-unmanned aerial vehicle edge computing network

Info

Publication number: CN115551013A
Application number: CN202211106470.7A
Authority: CN
Inventors: 邝祝芳; 王昊彬; 郭宇敬; 冯艳艳
Original assignee: Central South University of Forestry and Technology
Current assignee: Central South University of Forestry and Technology
Priority date: 2022-09-12
Filing date: 2022-09-12
Publication date: 2022-12-30

Abstract

The invention provides a method for deploying and unloading tasks of unmanned aerial vehicles in a multi-unmanned aerial vehicle edge computing network, aiming at maximizing the number of the tasks borne by the unmanned aerial vehicles. Mainly comprises the following steps: 1. and constructing a mathematical model P1 for unmanned aerial vehicle deployment and task unloading in the multi-unmanned aerial vehicle edge computing network. 2. Under the condition that the calculation frequency of a CPU (central processing unit) allocated to the task by the given unmanned aerial vehicle is given, a mathematical model P2 is constructed, the problem P2 is solved based on a differential evolution algorithm and a greedy algorithm, and the optimal position and elevation angle of the unmanned aerial vehicle, the transmission power of ground terminal equipment and the unloading decision of the task are solved. 3. And constructing a mathematical model P3 based on the obtained optimal position and elevation angle of the unmanned aerial vehicle and the transmission power of the ground terminal equipment, and obtaining the CPU calculation frequency and unloading decision of the unmanned aerial vehicle distributed to tasks. 4. And (5) circularly and iteratively solving between the step 2 and the step 3. 5. The application improves the task execution efficiency of the unmanned aerial vehicle in the multi-unmanned aerial vehicle edge computing network.

Description

Unmanned aerial vehicle deployment and task unloading method in multi-unmanned aerial vehicle edge computing network

Technical Field

The invention belongs to the technical field of wireless networks, and relates to a method for deploying unmanned aerial vehicles and unloading tasks in a multi-unmanned aerial vehicle edge computing network.

Background

With the development of the internet of things, wireless communication devices and wireless data traffic have increased geometrically. Especially in recent years, with the emergence of various computationally intensive and delay sensitive applications such as multimedia video streaming services, augmented reality, virtual reality, intelligent transportation, etc., it is important to provide a network with low delay, ultra-reliability, and high robustness. Cloud computing in a traditional core network is difficult to meet the requirements of service quality and service experience of terminal equipment due to long service delay and serious network congestion. Moving Edge Calculation (MEC) arises. The mobile edge computing is a network architecture which can realize cloud computing service on the edge side of the network, and can reduce time delay, improve efficiency and save power consumption, thereby improving service experience of users. But the deployment of MECs also has not minor drawbacks. First, MECs are expensive to deploy for hot spot areas of a city, such as commercial districts or densely populated areas. The network coverage is limited for rural areas, mountain areas, remote areas such as the sea and the like and areas which are easily affected by natural disasters, and edge unloading service is difficult to provide.

In recent years, unmanned aerial vehicles have been rapidly developed, and unmanned aerial vehicle edge computing provides a new solution for solving the above problems. The unmanned aerial vehicle edge computing refers to combining an edge computing architecture with an unmanned aerial vehicle platform, and the unmanned aerial vehicle can be used as a user node to unload a computing-intensive task to an edge server located on a ground base station, and can also be used as an aerial edge server to provide computing unloading service for a plurality of ground user nodes. Compared with ground communication, the unmanned aerial vehicle has the characteristic of flexibility, can provide anytime and anywhere mobile computing service even in mountainous areas, oceans and complex terrains, and provides spatial freedom. Meanwhile, the unmanned aerial vehicle can establish an air-ground line-of-sight link with the ground terminal equipment with a high probability, so that the quality of a communication link is improved, and the calculation performance is improved.

When the ground terminal equipment is numerous and the ground terminal equipment is required to execute tasks with large task amount and high calculation requirement, the limited calculation resource and coverage range of a single unmanned aerial vehicle can not meet the requirement of the ground terminal equipment, and multiple unmanned aerial vehicles can meet the requirement of the ground terminal equipment well. Therefore, when ground terminal equipment needs to execute huge calculation tasks, the unmanned aerial vehicle deployment decision-making method and the unmanned aerial vehicle resource allocation method aim at maximizing the number of the bearing tasks of the unmanned aerial vehicle according to the position of the terminal equipment, the channel state, the available CPU calculation resources of the unmanned aerial vehicle and other information.

In view of the above considerations, the present invention provides a method for unmanned aerial vehicle deployment and task offloading in a multi-unmanned aerial vehicle edge computing network.

Disclosure of Invention

The invention aims to solve the technical problem of providing a method for deploying and unloading tasks of unmanned aerial vehicles in a multi-unmanned aerial vehicle edge computing network. By jointly optimizing the task offloading decisions, resource allocation, and the position and elevation of the drone, the goal is to maximize the number of load-bearing tasks. The technical scheme of the invention is as follows:

a method for deploying unmanned aerial vehicles and unloading tasks in an edge computing network of multiple unmanned aerial vehicles comprises the steps of firstly constructing an unmanned aerial vehicle-assisted mobile edge computing system, wherein the system consists of M ground terminal devices and N unmanned aerial vehicles carrying edge servers, psi = {1,2, · i,.., M } represents a set of the ground terminal devices, phi = {1,2,.., j,..., N } represents a set of the unmanned aerial vehicles, and all the unmanned aerial vehicles are provided with directional antennas with adjustable beam widths. Assuming that each ground terminal device has 1 task at the current moment, the calculation task of the ground terminal device i e ψ can be executed locally or unloaded to the unmanned aerial vehicle for execution.

The invention provides a method for deploying unmanned aerial vehicles and unloading tasks in a multi-unmanned aerial vehicle edge computing network, which comprises the following steps: 1. a mathematical model of unmanned aerial vehicle deployment and task unloading in a multi-unmanned aerial vehicle edge computing network is established, and the method comprises the following steps:

the Task of each ground terminal device i epsilon psi is expressed as a binary Task _i ＝(C _i ，D _i ) In which C is _i Representing processing tasks Task _i The required CPU periodicity with the unit of cycles; d _i Task representation _i The unit is bit. (x) _i ，y _i ) Indicating the location, x, of the ground terminal equipment i e ψ _i And y _i The plane coordinates of the ground terminal equipment are all expressed in m, and the height is all 0 meter (m).

The 3-dimensional coordinates of each drone j ∈ φ are represented as (X) _j ，Y _j ，H _j ) Wherein X is _j And Y _j For the plane coordinate of unmanned plane j ∈ phi, H _j Height, in m, representing drone j ∈ φ. And the unmanned plane j epsilon phi is provided with a directional antenna with adjustable beam width. The azimuth angle and elevation angle half-power beam widths of the unmanned aerial vehicle j epsilon phi antenna are equal and are all 2 theta _j And e (0, pi) represents. Unmanned plane j belongs to phi position and elevation angle Q _j ＝(X _j ，Y _j ，H _j ，θ _j ) The position and elevation of all drones is denoted by Q.

a _i，j Task for Task _i Unload decision of a _i，j =0 for local calculation, a _i，j =1 denotes Task to be executed _i And unloading to unmanned plane j for calculation. The unloading of the ground terminal device task comprises two stages: 1) Ground terminal equipment i epsilon psi sends Task _i To drone j, 2) drone j allocates a computing resource computing task. Each ground terminal device is fixed in position before the mission is completed.

Task of S1-1 ground terminal equipment i epsilon psi _i Execute locally

Task of ground terminal equipment i belonging to psi _i The time of execution in the local is shown as (1):

wherein

And the CPU frequency (in cycles/s) of the local processing task of the ground terminal equipment i epsilon psi is shown.

Ground terminal equipment i belongs to psi and executes Task _i The energy consumption calculated locally is shown in (2):

wherein eta _l The effective capacitance coefficient represented by the ground terminal device i ∈ ψ depends on the chip architecture of the CPU.

S1-2 Task _i Offloading to unmanned aerial vehicle execution

S1-2-1 communication model

The plane distance between the ground terminal equipment i epsilon psi and the unmanned plane j epsilon phi is shown as (3):

unmanned plane j ₁ With unmanned plane j ₂ The distance between the planes is shown as (4):

unmanned plane j ₁ With unmanned plane j ₂ The distance between them is shown as (5):

the azimuth angle half-power wave beam width and the elevation angle half-power wave beam width of the unmanned plane j epsilon phi antenna are equal, and the antenna gain modeling in the azimuth angle theta direction and the elevation angle u direction is shown in (6):

wherein G is ₀ 2.2846, ω =0 represents the channel gain outside the antenna beam width. For simplicity, ω =0 is set.

The user i belongs to psi and unloads the task to the unmanned plane j belongs to phi, and then the user i belongs to psi

Must be within the coverage of drone j e phi, as shown in (7)

Channel gain g between ground terminal equipment i epsilon phi and unmanned aerial vehicle j epsilon phi _i，j As shown in (8):

wherein beta is ₀ Representing the channel power gain at a reference distance of 1 m.

The uplink transmission rate from the ground terminal device i e psi to the drone j e phi is shown as (9):

the uplink transmission power from the ground terminal device i epsilon psi to the drone j epsilon phi is shown as (10):

wherein p is _i，j Representing the transmission power (in W) from user i e ψ to drone j e. B represents the channel bandwidth between the ground terminal equipment i epsilon psi and the unmanned plane j epsilon phi, and the bandwidth between all the ground terminal equipment and the unmanned plane is equal and has the unit of Hz. N is a radical of ₀ Representing the noise power spectral density (in W/Hz).

The transmission time from the ground terminal equipment i epsilon phi to the unmanned aerial vehicle j epsilon phi for unloading the task is shown as (11):

the transmission energy from the ground terminal equipment i epsilon psi to unload the task to the unmanned aerial vehicle j epsilon phi is shown as (12):

s1-2-2 computational model

Task _i The time to unload to drone j e phi execution is shown as (13):

wherein

Indicates that the unmanned plane j belongs to phi and is allocated to the Task _i The CPU frequency (unit is cycles/s).

The energy consumption of the calculation executed by the task offloaded to the unmanned plane j ∈ phi is shown as (14):

wherein mu _c Representing the effective capacitance coefficient of the drone.

S1-3 problem description

Defining a mathematical model P1, and under the condition of meeting constraint conditions, maximizing the number of the bearing tasks of the unmanned aerial vehicle, wherein the model is as follows:

equation (15 a) is an objective function, χ = (F, a, Q, P) represents an optimization variable, where

Representing the CPU frequency allocation of the drone,

the decision to offload a task is made,

indicating the position and elevation of the drone,

representing the transmission power of the ground terminal equipment.

Equation (15 b) represents a completion time constraint for the task, both executed locally or on the drone, less than T _max 。

Equation (15 c) represents a maximum energy consumption constraint for executing the task, with energy consumption less than E for executing locally or on the drone _max 。

Equations (15 d) and (15 e) represent the maximum CPU computation frequency constraints of the ground terminal device and the drone, where

Is the maximum CPU computation frequency for the local computation,

is the CPU computation frequency of a single drone.

Equation (15 f) represents the unloading decision constraint of the ground terminal equipment, and each task can be only unloaded to one unmanned aerial vehicle.

Equation (15 g) represents the maximum transmission power constraint for uplink transmission in the system, where

Maximum transmission power when the task is uploaded.

Equation (15 h)) represents the coverage constraint of the drone to which a ground terminal device within the coverage of the drone can offload tasks.

Equation (15 i) represents the constraint of minimum distance between drones.

Equation (15 j) represents the constraint on the altitude of the drone.

Equation (15 k) represents the constraint on the elevation (half-power beamwidth) of the drone.

Expression (15 l) indicates that the coverage areas of the drones do not overlap.

P1 is a non-convex non-linear optimization problem, and therefore, the conventional optimization method cannot solve the problem. P1 is divided into 2 sub-problems, the first of which is the assignment of a given drone to a Task _i The CPU calculates the frequency F, solves the position and elevation angle Q of the unmanned aerial vehicle, the transmission power P of the ground terminal equipment and the unloading decision A of the unmanned aerial vehicle. The second sub-problem is to solve the final unloading decision a of the drone and the assignment of the drone to the Task given the location and elevation Q of the drone and the transmission power P of the ground terminal equipment _i The CPU of (1) calculates the frequency F. Let δ =1, δ denote the number of iterations of the whole, δ _max Represents the maximum iteration number, and O (delta) represents the number of tasks carried by the unmanned aerial vehicle after delta iterations

2. The steps of task unloading decision, optimal position and elevation angle of the unmanned aerial vehicle and transmission power of the ground terminal equipment based on a differential evolution algorithm and a greedy algorithm are as follows:

s2-1, constructing a mathematical model under the condition that the CPU of the unmanned aerial vehicle is assigned to each task to calculate the frequency F. And under the condition that the CPU calculation frequency F distributed to each task by the unmanned aerial vehicle is given, the unloading decision of the task, the optimal position and the elevation angle of the unmanned aerial vehicle and the transmission power of the ground terminal equipment are optimized, and a differential evolution algorithm and a greedy algorithm are adopted for solving. And solving the problem that the target is consistent with the problem P1, and maximizing the number of the bearing tasks of the unmanned aerial vehicle. The mathematical model P2 of the optimization problem can be written as follows:

(16a) For the objective function, (16 b) - (16 k) are constraints, Ω = (a, Q, P) where

Are the optimization variables.

S2-2, adopting a differential evolution algorithm and a greedy algorithm to solve unloading decision of tasks, optimal position and elevation angle of the unmanned aerial vehicle and transmission power of ground terminal equipment, and specifically comprising the following steps:

solving a problem P2, under the condition that the CPU calculation frequency F distributed to each task by the unmanned aerial vehicle is given, firstly, solving the position and the elevation angle Q of the unmanned aerial vehicle based on a differential evolution algorithm, solving the transmission power P of the ground terminal equipment and the unloading decision A of the task based on a greedy algorithm, and finally obtaining the maximum bearing task number of the unmanned aerial vehicle

Setting maximum iteration times tau of differential evolution algorithm _max =10000, and let τ =1 be the current iteration number.

The steps of solving the problem P2 by the differential evolution algorithm are as follows:

i) The population is initialized as follows:

a coding mechanism is proposed in which a population set represents

Wherein

Representing the set of position and elevation of the Tth iteration drone, Q _j (τ)＝(X _j (τ),Y _j (τ),H _j (τ),θ _j (τ)) represents the position and elevation coding for drone j ∈ φ, while noting Q _j (τ)＝q _j (X _j (τ),Y _j (τ),H _j (τ),θ _j (τ)) representing the position and elevation angle of the drone j ∈ Φ at the τ th iteration, and the value range is as follows:

wherein c is ₁ And 0 each represents X _j Upper and lower bounds of c ₁ Representing a constant in meters (m). c. C ₂ And 0 each represents Y _j Upper and lower bounds of c ₂ Denotes a constant in meters (m), H _max And H _min Respectively represent H _j Upper and lower bounds in meters (m), θ _max And theta _min Respectively represent theta _j An upper bound and a lower bound.

For convenience of description of X _j (τ),Y _j (τ),H _j (τ),θ _j (τ) value range, let us assume

The s decision variable representing the unmanned plane j belongs to phi, the value of s is {1,2,3,4 }, which respectively corresponds to Q _j X in (τ) _j (τ)，Y _j (τ)，H _j (τ)，θ _j (τ) that is

(17a) - (17 d) can be collectively expressed as follows:

for example when

In the formula (18)

Randomly generating a decision variable X _j (τ)，Y _j (τ)，H _j (τ)，θ _j The initial population of (τ) is calculated as follows:

where rand (0, 1) denotes a random selection of a constant from 0-1.

For example when

Time, randomly generate

The specific process of initializing the population comprises the following steps:

(1) let j =1,j denote the serial number of the drone, and randomly generate the position and elevation Q of drone j based on equation (20) _j (τ)＝(X _j (τ)，Y _j (τ)，H _j (τ)，θ _j (τ)), and Q is added _j (τ) put into the set of drone positions and elevations Q (τ) of the τ th iteration.

(2) Let iota =0, iota denote the generation of the j position and elevation Q of the drone _j Number of formation of (. Tau.),. Iota _max =200 denotes randomly generating drone j position and elevation Q _j (τ) maximum number of generations.

(3) Randomly generating position and elevation angle Q of unmanned aerial vehicle j +1 _j+1 (τ), iota = iota +1. Judging whether the position of each unmanned aerial vehicle in the unmanned aerial vehicle j +1 and the unmanned aerial vehicle position and elevation angle set Q (tau) of the tau iteration meets constraint expressions (16 g) and (16 j), namely Q (tau) and Q _j+1 Whether or not the position of (τ) satisfies the constraint equation (16 g) and the equation (16 j). The judgment and selection are as follows:

if Q (τ) and Q _j+1 (τ) satisfies the constraint equations (16 g) and (16 j), which indicates Q (τ) and Q _j+1 (τ) distance between drones is greater than or equal to the nearest distance limit of drones

I.e. no interaction between drones in drones j +1 and Q (τ)Collision, and the coverage of drones j +1 and Q (τ) do not intersect, then let j = j +1, let Q be _j (tau) putting the unmanned aerial vehicle position and elevation angle set Q (tau), and skipping to the step (4). If Q (τ) and Q _j+1 (τ) does not satisfy constraint equation (16 f) and equation (16 j), indicating that the generation of the j +1 st drone position was unsuccessful. Iota is less than or equal to _max And (4) if the answer is positive, skipping to the step (3) if the answer is positive, otherwise skipping to the step (1).

(4) And (4) judging whether j is less than or equal to N, and if so, returning to the step (2). Otherwise, the positions and the elevation angles of all the drones are successfully generated, and the initial population Q (tau) of the drones is obtained.

ii) calculating the transmission power of the ground terminal equipment according to the new position and elevation angle of the unmanned aerial vehicle, and the steps are as follows:

and according to the position and the elevation angle of the unmanned aerial vehicle j epsilon phi and the position information of the user i epsilon psi, finding out the coverage range of which unmanned aerial vehicle the ground terminal equipment i epsilon psi is in through an equation (16 f). Calculating the frequency F and the maximum time delay T of the CPU assigned to a task for a given drone according to equation (16 b) _max And obtaining the transmission rate required by the ground terminal equipment i epsilon psi to the unmanned aerial vehicle, wherein the transmission rate meets the following constraint:

as can be seen from the analysis formula (21), the transmission power of the ground terminal equipment must satisfy the formula (21), and meanwhile, the transmission power of the ground terminal equipment must also satisfy the formula (16 c), so that the equation (21) takes the equal sign as the optimal value of the transmission power of the ground terminal equipment.

Based on (21) and (10), the transmission power p of the tau iteration terrestrial terminal equipment i epsilon psi can be calculated _i，j (τ) is represented by formula (22):

iii) Calculating the unloading decision of the task according to the transmission power of the ground terminal equipment and the new position and elevation angle of the unmanned aerial vehicle, and comprising the following steps:

dividing the task set psi into psi ₁ 、ψ ₂ 、ψ ₃ Three categories, and satisfy ψ = ψ ₁ ∪ψ ₂ ∪ψ ₃ 。

Wherein the first type task psi ₁ Having the highest priority, ground terminal equipment i epsilon psi ₁ Indicating that it is not within the coverage of the drone, task at this time _i Can only be done locally, in which case the unload decision a for the # th iteration _i，j (τ)＝0。

Task psi of the second type ₂ At this time, the ground terminal equipment i is epsilon psi ₂ In the coverage of unmanned aerial vehicle, task _i The method can be unloaded to an unmanned aerial vehicle for execution, and the tau-th iteration ground terminal equipment i epsilon psi can be calculated based on the transmission power obtained in the step ii) ₂ Transmission rate r to drone j _i，j (τ). Unmanned aerial vehicle assignment to Task _i Under the condition that the calculation resources satisfy the formulas (16 b) and (16 c), the unloading decision is solved based on a greedy algorithm, and the selection strategy of the greedy algorithm is that the ground terminal equipment i belongs to psi ₂ Transmission rate r to drone j _i，j (τ), i.e. transmission rate r _i，j (τ) fastest is selected first, with the unload decision a of the τ th iteration _i，j (τ)＝1。

Task type III ₃ That is, after the unmanned aerial vehicle computing resources are fully loaded, the tasks can only be performed locally, namely, the total task psi is divided by psi ₁ 、ψ ₂ Task outside, unload decision a for the τ th iteration at this time _i，j (τ)＝0。

iv) calculating a target value

Obtaining j epsilon phi position and elevation angle of unmanned aerial vehicle of the tau iteration based on the steps ii) and iii)

The transmission power of the ground terminal equipment and the unloading decision of the task can obtain the result { P (tau), Q (tau), A (tau) } of the tau-th iteration, wherein P (tau) represents the transmission power of the ground terminal equipment of the tau-th iteration, and Q (tau) represents the position set of the tau-th iteration unmanned aerial vehicleIn sum, a (τ) represents the task unload decision for the τ -th iteration. Calculating a target value of the tau iteration based on the result of the tau iteration, namely the maximum number of bearing tasks of the unmanned aerial vehicle

v) after determining the position and the elevation angle of the tau-th iteration unmanned aerial vehicle, performing cross mutation operation, wherein the steps are as follows:

mutation operation: according to

Is provided with

For the j epsilon phi position and elevation angle of the unmanned aerial vehicle obtained after the tau-th iterative variation,

respectively correspond to

By mutation operations of

The calculation formula of (a) is as follows:

equation (23) represents the position and elevation q for the tau-th iteration for drone j ∈ phi _j (X _j (τ)，Y _j (τ)，H _j (τ)，θ _j (τ)) performing a mutation operation, wherein j ₁ 、j ₂ 、j ₃ E phi represents that 3 different numbers are randomly selected in the unmanned aerial vehicleτ denotes Q in a differential evolution algorithm _j F denotes the scaling factor, taking F =0.9.

And (3) cross operation: is also provided with

Represents the j ∈ phi position and elevation angle of the unmanned plane obtained after the tau-th iteration crossing according to

And with

Is selected by cross probability to obtain

Wherein

The calculation formula of (c) is as follows:

equation (24) represents the operation of crossing the tau-th iteration for drone j e phi position and elevation, CR represents the probability of crossing, taking CR =0.9.

Through mutation and crossing to obtain

Finally obtaining a population U (tau) = { U = [) ₁ (τ)、U ₂ (τ)、…U _j (τ)、…U _N (τ) }. Steps ii) -iii) determining a new { P } ^* (τ)、Q ^* (τ)、A ^* (τ) }, step iv) obtaining the target value L ^* (τ)。

vi) the selection operation is as follows:

selection based on greedy thought, i.e.The largest of the target values is selected as the new individual. Crossing the variation to obtain a population U (tau) = { U = [ (U) ] ₁ (τ)、U ₂ (τ)、…U _j (τ)、…U _N (τ) } and the original population Q (τ) = { Q ₁ (τ)、Q ₂ (τ)、…Q _j (τ)、…Q _N (τ) }, the comparison formula is shown as formula (25):

comparison L ^* (τ) and L (τ), the steps are as follows:

if L ≧ L (τ) indicates that the population obtained after the cross mutation operation is better, { P (τ + 1), Q (τ + 1), a (τ + 1) } = { P ^* (τ)、Q ^* (τ)、A ^* (τ) }, if L ^* (τ) < L (τ), then { P (τ + 1), Q (τ + 1), a (τ + 1) } = { P (τ), Q (τ), a (τ) } is unchanged.

vii) judgment of τ +1 > τ _max And if yes, stopping loop iteration, outputting { P (tau + 1), Q (tau + 1) and A (tau + 1) }, otherwise, tau = tau +1, and jumping to the step v).

3. According to the position and elevation angle Q of the unmanned aerial vehicle obtained in the step 2 and the transmission power P of the ground terminal equipment, solving a final unloading decision A of the unmanned aerial vehicle and a Task allocated to the unmanned aerial vehicle _i The CPU calculates the frequency F, and the solving steps are as follows:

s3-1, solving an unloading decision and calculating resource allocation of the unmanned aerial vehicle, wherein the aim is to maximize the number of bearing tasks of the unmanned aerial vehicle, and a mathematical model P3 of an optimization problem can be written in the following form:

wherein x ₁ = (A, F), wherein

The following equations (8), (9), (11) and (12) show

The portion is a known value, i.e., a constant.

And S3-2, after the position and the elevation angle Q of the unmanned aerial vehicle and the transmission power P of the ground terminal equipment are obtained according to the step 2, solving an unloading decision A of the task and a calculation resource distribution F of the unmanned aerial vehicle by adopting a convex optimization method.

The specific operation of S3-2-1 non-convex-to-convex is as follows:

i) Order to

And

expressing expressions (26 b) and (26 c), respectively, and obtaining hessian matrices of (26 b) and (26 c) as follows:

as can be seen from the analysis, since both equations (27 a) and (27 b) are non-positive definite matrices, (26 b) and (26 c) are non-convex constraints.

ii) carrying out a non-convex-to-convex transformation operation by a linearization constraint factor, comprising the following steps:

the equation (26 b) is first linearized, and a small variable ε is introduced in order to avoid the denominator being zero ₁ Equation (26 b) can be restated as:

an auxiliary variable gamma is defined _i，j The method comprises the following steps:

substituting formula (29) into formula (28) to give formula (30):

substituting formula (29) into formula (26 e) to give formula (31):

since equation (26 e) represents the maximum CPU calculation frequency of the drone, it can be obtained

Also, because of the formula (29), can obtain

And replace

In (1)

The formula (32) can be obtained finally:

then model P3 may be rewritten to model P4 as follows:

since (33 b) and (33 c) are also non-convex, the equations (33 b) and (33 c) are relaxed as follows:

(1) for the relaxation operation of equation (33 b), the procedure is as follows:

due to the offload decision a _i，j E (0, 1) is a discrete variable, thus relaxing a _i，j E (0, 1), as shown in (34):

for formula (34), define

From the equations (32) and (34), the constraint factor product ω can be obtained _i，j ：

By using

Substitution of equation (35) yields equation (36) as follows:

(2) for the relaxation operation of formula (33 c), the procedure is as follows:

definition of

Because of

Therefore, it is not only easy to use

Then σ can be obtained _i，j The ranges of (a) and (b) are as follows:

definition of

From equations (34) and (37), the constraint factor product can be obtained

By using

Alternative (38), resulting in equation (39), shown below:

model P4 can be transformed into P5 as follows:

(38)，(39) (40g)

wherein

Because of the fact that

Therefore, it is possible to

And

the trend of (1) is the same, so the target formula is changed to

A mathematical model P6 was obtained as follows:

S.t. (40b)，(40c)，(40d)，(40e)，(40f)，(40g) (41b)

s3-2-2: adopting a KKT condition to solve the calculation frequency of the unloading decision and the task of the unmanned aerial vehicle, and specifically comprising the following steps:

i) Solving the problem P6, constructing the Lagrangian function and dual problem of P6, and ordering

Wherein A is ₁ Represents the task unloading decision of the model P6 through convex optimization,

lagrange multipliers of expressions (40 b) - (40 c),

the Lagrangian multiplier of expression (40 d),

a Lagrangian multiplier represented by the formula (40 e),

a Lagrangian multiplier of expression (40 f),

the lagrange multipliers respectively expressed by the formula (40 g),

lagrange multipliers respectively representing formula (40 j), then

The lagrangian function of problem P6 is as follows:

the dual function of the mathematical model P6 is defined as

The dual problem is that

ii) Lagrangian function (42) for a _i，j ，

Calculating a partial derivative, wherein the steps are as follows:

lagrangian function (42) for a _i，j The partial derivatives are calculated as follows:

lagrange function (42) pair

The partial derivatives are calculated as follows:

lagrange function (42) pair

The partial derivatives are calculated as follows:

lagrange function (42) pairs

The partial derivatives are calculated as follows:

lagrange function (42) pair

The partial derivatives are calculated as follows:

lagrange function (42) pairs

The partial derivatives are calculated as follows:

lagrange function (42) pair

The partial derivatives are calculated as follows:

iii) The conditions according to KKT are as follows:

from equation (43), equation (50) can be derived, as follows:

formula (51) is obtainable from formula (44):

formula (52) is obtained according to formula (45):

equations (53) and (54) are obtained from equations (46) and (47):

finding gamma in equation (36) _i，j 、ω _i，j While the related equation can be found:

therefore, it can be analyzed from the formulas (55) and (56) that (53) and (54) are γ, respectively _i，j Upper and lower bounds of (a) if gamma _i，j When the value between (52) and (53) does not take the boundary, then

And with

Are both 0.

Equations (57) and (58) are obtained from equations (48) and (49):

the same can be found in equation (39) _i，j 、

While the related equation can be found:

therefore, the (57) and (58) can be analyzed according to the formulas (59) and (60)Other is σ _i，j Upper and lower bound of (a), if _i，j In the case that the value between (57) and (58) does not take the boundary, then

And with

Are both 0.

By analyzing (40 d), (40 e), (40 f) and (40 g), the results were obtained

Since the portion is not 0, according to the KKT condition,

the section is 0. While not taking sigma _i，j And gamma _i，j The boundary of (2) is then

All are 0, initialization is performed so that i =1.

Equation (50) can be simplified to (61):

iv) initialization

Respectively corresponding to convergence accuracy xi ₁ 、ξ ₂ ρ is the number of iterations, let ρ =0, and the initial value is

v) obtaining a obtained from the rho-th iteration according to the formulas (51), (52) and (61) _i，j (ρ)、ω _i，j (ρ)、

At this time

The cases of (c) are as follows:

calculating Lagrange function according to equations (44) and (45)

The value of (c).

vi) updating Lagrange multiplier based on gradient descent method according to (44) and (45)

As follows:

vii) judgment of a _i，j (ρ)-a _i，j (ρ -1) > 0, if yes, step v) is skipped, otherwise step viii) is skipped.

viii) judging whether i > M is satisfied, if not, i = i +1, turning to step iv), otherwise, outputting A ₁ 、ω _i，j 、

ix) calculating assignment of Task unmanned aerial vehicle j to Task _i The calculation frequency of (c):

by passing

Can find gamma _i，j The formula is as follows:

the Task can be obtained by the equations (29) and (48) _i Is calculated frequency of

The formula is as follows:

x) by A ₁ The offloading decision a is obtained as follows:

wherein A (a) _i，j ) Representing a in the set of offload decisions A _i，j ，A ₁ (a _i，j ) Representing offload decision set A ₁ A in _i，j 。

S3-2-3 by

And obtaining a final unloading decision A, which comprises the following steps:

by A ₁ Reselecting an unloading decision A, starting to select j =1 from a first unmanned aerial vehicle, and specifically comprising the following steps:

i) Reselecting the unloading decision A through the residual calculation resources of the unmanned aerial vehicle, and comprising the following steps:

ii) pair

And (4) judging, wherein the judging step is as follows:

a if

The steps are as follows:

(1) selection A ₁ 0 in (A) ₁ (a _i，j ) The value in the interval < 0.5, and secondly recording a in this interval _i，j Task corresponding to the minimum value of

Is recorded as i ₁ . Let A (a) _i，j )＝1，A ₁ (a _i，j ) =0. Is newly paired by the formula (51)

And (6) performing operation.

(2) If it is

Then the

Judgment of 0 < A ₁ (a _i，j ) If < 0.5 is an empty set, the empty set jumps to step ii). Otherwise, returning to the step i).

(3) If it is

If 0 < A ₁ (a _i，j ) If < 0.5 is empty set, jump to step iii). Go back to step i)

b is if

The steps are as follows:

first, A is selected ₁ A in the total is more than or equal to 0.5 ₁ (a _i，j ) The value in the interval less than or equal to 1 is recorded _i，j Task of maximum value of

Record as

Order to

Is re-paired by the formula (51)

Carry out the operation if

Then the

If it is

And returning to the step i) again.

iii) Let j = j +1, when j > N, then obtain a final unloading decision a, and the CPU computation frequency allocated to the upload task by the drone is F.

iv) calculating

And O (delta) represents the number of the tasks carried by the unmanned aerial vehicle after delta iterations, and the values of the results F, A, Q and P of the optimization variables are obtained according to P2 and the formula (67).

4. Comparing O (δ) with O (δ + 1), if O (δ 0+ 1) > O (δ 1), O (δ + 1) = O (δ + 1), and recording F, a, Q, P for O (δ + 1), otherwise O (δ + 1) = O (δ), maintaining F, a, Q, P for O (δ). Judging that delta +1 is larger than delta _max And if not, making delta = delta +1, skipping to the step 2 for a new iteration based on the calculated F, and if so, ending the iteration to obtain F, A, Q and P of the optimized variables and the maximum bearing task number O (delta) of the unmanned aerial vehicle.

Advantageous effects

The invention provides a method for deploying unmanned aerial vehicles and unloading tasks in a multi-unmanned aerial vehicle edge computing network. Effectively obtain unmanned aerial vehicle's maximize and bear the weight of the task number.

Drawings

FIG. 1 is a schematic view of a scene model of the present invention;

fig. 2 is a flowchart of a method for deploying unmanned aerial vehicles and unloading tasks in a multi-unmanned aerial vehicle edge computing network according to the present invention;

FIG. 3 is a flow chart of the present invention for solving for transmission power, UAV position, and elevation;

FIG. 4 is a flow chart of the present invention for offloading decisions to solve a task and for unmanned aerial vehicle CPU calculation frequency;

Detailed Description

The invention will be described in further detail below with reference to the following figures and specific examples:

example 1:

l1 in this embodiment, fig. 1 is a schematic view of an unmanned aerial vehicle edge computing scene model, which includes N =4 unmanned aerial vehicles, is equipped with an edge server, has M =15 ground terminal devices, and has 1 task on each user. The Task of the ground terminal equipment is described as Task _i ＝(C _i ，D _i ). The maximum CPU frequency of the ground terminal equipment is

The maximum CPU frequency of the edge server is

Setting the maximum completion time T of each task _max =1s, maximum energy consumption E _max =1J. Let the transmission bandwidth be B =1MHZ, noise power N ₀ ＝10 ^-20W /Hz, channel power gain at reference distance β =1.42 × 10 ^-4 ，G ₀ =2.2846 is a normal number, maximum transmission power P _max =1.5w. Minimum distance between unmanned aerial vehicles

Effective capacitance coefficient eta of unmanned aerial vehicle and terminal equipment ₁ ＝10 ^-27 ，η ₂ ＝10 ^-28 。

L1-1 initializes the location of the ground terminal and its task attributes, and the CPU computation frequency assigned to the task. Wherein position x _i 、y _i Task _i C of (A) _i And D _i The value ranges of (a) are shown in table 1, the value ranges of the parameters of the unmanned aerial vehicle are shown in table 2, the attribute information of the task is shown in table 3, the calculation frequency initially allocated to the task CPU is shown in table 4, the iteration number δ =1, and the initialization target value (the maximum number of the tasks carried by the unmanned aerial vehicle) O (δ -1) =0.

TABLE 1 parameter ranges for tasks

	x(m)	y(m)	C(cycles)	D(bits)
					Min	0	0	1600000000	819200
Max	100	100	16000000000	8192000

Table 2 parameter ranges for unmanned aerial vehicles

X(m)	Y(m)	H(m)	θ
				Min
0	0	50	π/6
				Max	100	100	100	π/2

TABLE 3 parameter Table for randomly generated tasks

	x _i (m)	y _i (m)	C _i (cycles)	D _i (bits)
					Task ₁	34.9624	21.4531	333464936.6	3725299.33
Task ₂	29.4299	7.2419	1373386716	4722915.82
					Task ₃	33.1190	40.7013	431874596.5	4982733.66
Task ₄	61.0522	1.6279	1016263899	1614420.64
					Task ₅	90.6348	12.4428	1220885273	4668529.18
Task ₆	4.6360	48.3225	1591534450	5971805.43
					Task ₇	85.7288	99.9832	1450304267	7445636.2
Task ₈	13.9110	54.1779	603781186.8	4510664.35
					Task ₉	72.2903	6.4391	641641188.4	7501226.7
Task ₁₀	91.5294	65.2428	878464385.9	3172692.16
					Task ₁₁	12.8824	0.8689	333843880	1578423.87
Task ₁₂	60.2404	89.2471	1340989081	4741559.12
					Task ₁₃	15.3078	55.4631	806503241.9	883570.39
Task ₁₄	21.3960	57.7343	864337501.5	7156238.06
					Task ₁₅	13.5097	37.2678	678734350.8	6822526.04

TABLE 4 initialize CPU computation frequencies assigned to tasks

	Initializing CPU computation frequencies (cycles/bit) assigned to tasks
		Task ₁	444619915.5
Task ₂	1831182288
		Task ₃	575832795.3
Task ₄	1355018532
		Task ₅	1627847030
Task ₆	2122045933
		Task ₇	1933739023
Task ₈	805041582.3
		Task ₉	855521584.5
Task ₁₀	1171285848
		Task ₁₁	445125173.4
Task ₁₂	1787985441
		Task ₁₃	1075337656
Task ₁₄	1152450002
		Task ₁₅	904979134.3

L2, solving the optimal position and elevation angle Q of the unmanned aerial vehicle and the transmission power P of the ground terminal equipment based on differential evolution and greedy algorithm:

and L2-1 converts the optimization problem P1 into an optimization problem P2 under the condition of given calculation frequency, and solves the optimization problem P2 by utilizing differential evolution and a greedy algorithm.

L2-2-1 constructs an initial population Q (τ) of P2 drones by equation (20) and table 2 and let τ =1.

TABLE 5 initial population of unmanned aerial vehicles Q (τ)

	X(m)	Y(m)	H(m)	θ
					j＝1	71.02	75.39	52.35	π/5.47
j＝2	7.25	2.93	66.52	π/5.88
					j＝3	81.40	0.43	68.47	π/5.73
j＝4	3.35	85.79	58.08	π/5.59

L2-2-2 obtains the transmission power P (tau) of the ground terminal equipment through a critical boundary according to the formula (22) and the initial population Q (tau).

TABLE 6 Task _i Transmission power p of _i,j (τ)

L2-2-3 determines the unloading decision A (tau) according to the initial population Q (tau) and the table 7.

TABLE 7 Task _i Is unloaded decision A (tau)

	a _i,1	a _i,2	a _i,3	a _i,4
					Task ₁	0	0	0	0
Task ₂	0	1	0	0
					Task ₃	0	0	0	0
Task ₄	0	0	0	0
					Task ₅	0	0	1	0
Task ₆	0	0	0	0
					Task ₇	0	0	0	0
Task ₈	0	0	0	1
					Task ₉	0	0	0	0
Task ₁₀	1	0	0	0
					Task ₁₁	0	0	0	0
Task ₁₂	1	0	0	0
					Task ₁₃	0	0	0	0
Task ₁₄	0	0	0	0
					Task ₁₅	0	0	0	0

L2-2-4 finds the task target L =5 from the unload decision a (τ).

L2-2-5 was subjected to crossover and mutation operations according to the formulas (22) and (23) to obtain tables 8 and 9, which are shown in the following tables

And with

TABLE 8 results from crossover operations

	X(m)	Y(m)	H(m)	θ
					j＝1	77.89	75.00	60.87	π/5.48
j＝2	20.50	9.79	73.62	π/5.85
					j＝3	74.53	0.81	59.95	π/5.72
j＝4	24.01	64.78	81.21	π/6

TABLE 9 results of mutation operations

	X(m)	Y(m)	H(m)	θ
					j＝1	77.89	75.00	60.87	π/5.48
j＝2	20.50	9.79	73.62	π/5.85
					j＝3	74.53	0.81	59.95	π/5.71
j＝4	24.01	64.78	58.08	π/5.87

L2-2-6 from rand (0, 1) =0.7, U (τ) = Q can be obtained ^* (τ) for new ground terminal equipmentTransmission power P ^* (τ) and offload decision A ^* (τ) obtaining an evaluation L of the individuals ^* (τ)＝8。

L2-2-7 reacting L (. Tau.) with L ^* Making a comparison if L (tau) < L ^* (τ), then A (τ + 1) = A ^* (τ)、P(τ+1)＝P ^* (τ)、Q(τ+1)＝Q ^* (τ) if L (τ) ≧ L ^* (τ), then a (τ + 1) = a (τ), P (τ + 1) = P (τ), Q (τ + 1) = Q (τ).

L2-2-8 judges whether tau is more than or equal to 1000, if yes, iteration is finished, and the optimal solution is obtained; if not, continue τ = τ +1 to L2-2-5.

L2-3 calculated the values of Q and P as shown in tables 10 and 11.

TABLE 10 position Q (τ) of drone by differential evolution _max )

	X(m)	Y(m)	H(m)	θ
					j＝1	77.89	75.00	60.87	π/5.48
j＝2	20.50	9.79	73.62	π/5.85
					j＝3	74.53	0.81	59.95	π/5.71
j＝4	24.01	64.78	81.21	π/5.87

TABLE 11 Task _i Transmission power P (τ) _max )

L3, solving an unloading decision and calculating a frequency scheme according to a convex optimization method:

l3-1 constructs a problem according to step S3-2-1 using a linearized approach to problem P3, constructing convex problem P6.

L3-2 calculates the solving convex problem P6 for each task using the KKT condition for each task separately according to step ii) in S3-2-2. Task based on KKT condition calculation ₂ The computation is transmitted to the unmanned aerial vehicle for execution,

ξ ₁ ＝10 ^-2 、ξ ₂ ＝10 ^-2 ，a _2，2 the results are shown in the tableShown at 12. Task computing completion Task _i Offload decision a ₁ As shown in Table 13, the relaxation variable γ _i，j 、

σ _i，j 、ω _i，j As shown in tables 14, 15, 16 and 17.

Table 12 Task uploaded to unmanned aerial vehicle ₂

TABLE 13 Task _i Offload decision a ₁

	a _i，1	a _i，2	a _i，3	a _i，4
					Task ₁	0.00	0.00	0.00	0.00
Task ₂	0.00	0.79	0.00	0.00
					Task ₃	0.37	0.00	0.00	0.00
Task ₄	0.00	0.00	0.73	0.00
					Task ₅	0.00	0.00	0.00	0.00
Task ₆	0.00	0.00	0.00	0.00
					Task ₇	0.00	0.00	0.00	0.00
Task ₈	0.00	0.00	0.00	0.45
					Task ₉	0.00	0.00	0.00	0.00
Task ₁₀	0.52	0.00	0.00	0.00
					Task ₁₁	0.00	0.43	0.00	0.00
Task ₁₂	0.71	0.00	0.00	0.00
					Task ₁₃	0.00	0.00	0.00	0.49
Task ₁₄	0.00	0.00	0.00	0.49
					Task ₁₅	0.00	0.44	0.00	0.00

TABLE 14 Task _i Gamma of (2) _i，j

TABLE 15 Task _i Is/are as follows

TABLE 16 Task _i Sigma of _i，j

TABLE 17 Task _i Omega of _i，j

	ω _i，1	ω _i，2	ω _i，3	ω _i，4
					Task ₁	0.00	4.2×10 ^-10	0.00	0.00
Task ₂	6.2×10 ^-10	0.00	0.00	0.00
					Task ₃	0.00	0.00	5.56×10 ^-10	0.00
Task ₄	0.00	0.00	0.00	0.00
					Task ₅	0.00	0.00	0.00	0.00
Task ₆	0.00	0.00	0.00	0.00
					Task ₇	0.00	0.00	0.00	0.00
Task ₈	0.00	0.00	0.00	5.27×10 ^-10
					Task ₉	0.00	0.00	0.00	0.00
Task ₁₀	4.25×10 ^-10	0.00	0.00	0.00
					Task ₁₁	0.00	1.05×10 ^-9	0.00	0.00
Task ₁₂	3.84×10 ^-10	0.00	0.00	0.00
					Task ₁₃	0.00	0.00	0.00	5.61×10 ^-10
Task ₁₄	0.00	0.00	0.00	3.93×10 ^-10
					Task ₁₅	0.00	4.53×10 ^-10	0.00	0.00

The calculation frequency F of the unmanned aerial vehicle based on P and Q and allocated to the uploading task is obtained by the L3-3 according to the step ix) and the step x) in the S3-2-2 and is shown in a table 19, and the unloading decision A obtained by convex optimization is shown in a table 18.

And L3-4 obtains a final task unloading decision A according to S3-2-3, and obtains the calculation frequency F of the corresponding uploading task.

TABLE 18 Task _i Offload decision a

TABLE 19 Task _i Is calculated at a frequency F

L3-5 outputs the obtained unloading decisions A and F, and calculates a target value, namely the maximum number of the bearing tasks

L4-1 compares O (delta-1) =0 and O (delta) =9, if O (delta) ≧ O (delta-1), the O (delta) is kept unchanged, and the corresponding P, F, A, Q of O (delta) are recorded. If O (δ) < O (δ -1), O (δ) = O (δ -1), and the corresponding P, F, A, Q of O (δ -1) is recorded, let δ = δ +1.

L4-2 is equal to or greater than delta _max And if not, stopping the loop iteration to output { P, F, A, Q, O (delta) }, obtaining the final { P, F, A, Q, O (delta) }, and if not, returning to the step S2.

Passing through delta _max Obtaining O (delta) after the optimization of the second iteration _max ) =15, the unmanned aerial vehicle position and elevation angle Q, the task offloading decision a, the calculated CPU frequency F, and the transmission power P of the ground terminal device are obtained at the same time, as shown in tables 20, 21, 22, and 22.

TABLE 20 offload decision A for task

	a _i，1	a _i，2	a _i，3	a _i，4
					Task ₁	1	0	0	0
Task ₂	0	0	0	1
					Task ₃	1	0	0	0
Task ₄	0	1	0	0
					Task ₅	0	1	0	0
Task ₆	1	0	0	0
					Task ₇	0	0	1	0
Task ₈	1	0	0	0
					Task ₉	0	1	0	0
Task ₁₀	0	0	1	0
					Task ₁₁	0	0	0	1
Task ₁₂	1	0	0	0
					Task ₁₃	1	0	0	0
Task ₁₄	1	0	0	0
					Task ₁₅	1	0	0	0

TABLE 21 CPu calculation frequency F assigned to a task

TABLE 22 Transmission Power P of ground terminal equipments

	Transmission power (W)
		Task ₁	0.025185832
Task ₂	0.015680924
		Task ₃	0.051279243
Task ₄	1.47
		Task ₅	0.014263526
Task ₆	0.941542811
		Task ₇	1.5
Task ₈	0.014619506
		Task ₉	1.49
Task ₁₀	0.000301841
		Task ₁₁	1.48
Task ₁₂	0.863828479
		Task ₁₃	0.00054
Task ₁₄	1.5
		Task ₁₅	1.48

Table 23 optimal position Q of drone

	X(m)	Y(m)	H(m)	θ
					j＝1	38.14	58.31	67.19	π/5.36
j＝2	74.61	18.54	59.32	π/5.83
					j＝3	98.30	99.14	60.60	π/5.69
j＝4	0.55	2.81	50.31	π/5.65

Claims

1. The unmanned aerial vehicle deployment and task unloading method in the multi-unmanned aerial vehicle edge computing network comprises the following steps:

step 1: and constructing a mathematical model P1 of the ground terminal equipment task in the multi-unmanned-aerial-vehicle edge computing network.

Step 2: given the CPU calculation frequency F assigned to each task by the unmanned aerial vehicle, a mathematical model P2 is constructed. And solving a problem P2 by adopting a method of combining a differential evolution algorithm and a greedy algorithm, and solving the optimal position and elevation angle Q of the unmanned aerial vehicle, the transmission power P of the ground terminal equipment and the unloading decision A of the task.

And step 3: and (3) constructing a mathematical model P3 according to the optimal position and elevation angle Q of the unmanned aerial vehicle obtained in the step (2) and the transmission power P of the ground terminal equipment, completing non-convex-to-convex conversion by a linearization constraint factor method, constructing a mathematical model P6, solving and obtaining the CPU calculation frequency F and the unloading decision A which are distributed to tasks by the unmanned aerial vehicle through a convex optimization method, calculating the maximum bearing task number of the unmanned aerial vehicle, and marking the target value as L.

And 4, step 4: setting a maximum number of iterations δ _max And =100, making the current iteration number delta =0, circularly iterating between the step 2 and the step 3, making delta = delta +1 every time iteration is carried out, comparing the maximized bearing task number of the unmanned aerial vehicle in the iteration, selecting the maximized bearing task number O (delta), and circularly iterating to delta _max The final result converges and the maximum number of bearer tasks O (delta) is obtained _max )。

Step 1, the steps of constructing a mathematical model of unmanned aerial vehicle deployment and task unloading in a multi-unmanned aerial vehicle edge computing network are as follows:

the Task of each ground terminal device i epsilon psi is expressed as a binary Task _i ＝(C _i ，D _i ) In which C is _i Representing processing tasks Task _i The required CPU periodicity is expressed in cycles; d _i Task representation _i The unit is bit. (x) _i ，y _i ) Indicating the location, x, of the ground terminal equipment i e ψ _i And y _i The plane coordinates of the ground terminal equipment are all expressed in m, and the height is all 0 meter (m).

The 3-dimensional coordinates of each drone j ∈ φ are represented as (X) _j ，Y _j ，H _j ) Wherein X is _j And Y _j Is the plane coordinate of the unmanned plane j epsilon phi, H _j The height of the unmanned plane j epsilon phi is expressed, and the unit isAnd m is selected. And the unmanned plane j epsilon phi is provided with a directional antenna with adjustable beam width. The azimuth angle and elevation angle half-power beam widths of the unmanned aerial vehicle j epsilon phi antenna are equal and are all 2 theta _j And e (0, pi) represents. Position and elevation angle Q of unmanned aerial vehicle j epsilon phi _j ＝(X _j ，Y _j ，H _j ，θ _j ) The positions and elevation angles of all drones are denoted by Q.

a _i，j Task _i Unload decision of a _i，j =0 for local calculation, a _i，j =1 denotes Task to be executed _i And (5) unloading to unmanned plane j for calculation. The unloading of the ground terminal device task comprises two stages: 1) Ground terminal equipment i epsilon psi sends Task _i To drone j, 2) drone j allocates a computing resource computing task. Each ground terminal device is fixed in position before the mission is completed.

Task of S1-1 ground terminal equipment i epsilon psi _i Execute locally

Task of ground terminal equipment i epsilon psi _i The time of execution in the local is shown as (1):

wherein

Ground terminal equipment i epsilon psi executing Task _i The energy consumption calculated locally is shown in (2):

wherein eta _l The effective capacitance coefficient represented by the ground terminal device i epsilon psi depends on the chip architecture of the CPU.

S1-2 Task _i Offloading to drone execution

S1-2-1 communication model

The plane distance between the ground terminal device i epsilon psi and the unmanned aerial vehicle j epsilon phi is shown as (3):

unmanned plane j ₁ With unmanned plane j ₂ The distance between the two is shown as (5):

Must be in the coverage area of drone j ∈ φ, as shown in (7)

Channel gain g between ground terminal equipment i epsilon psi and unmanned aerial vehicle j epsilon phi _i，j As shown in (8):

The uplink transmission rate from the ground terminal device i epsilon psi to the drone j epsilon phi is shown as (9):

the uplink transmission power from the ground terminal device i e ψ to the drone j e φ is as shown in (10):

wherein p is _i，j Representing the transmission power (in W) from user i e v to drone j e. B represents the channel bandwidth between the ground terminal equipment i epsilon phi and the unmanned aerial vehicle j epsilon phi, the bandwidth between all the ground terminal equipment and the unmanned aerial vehicle is equal, and the unit is Hz. N is a radical of ₀ Representing the noise power spectral density (in W/Hz).

The transmission time from the ground terminal equipment i epsilon psi to the unmanned aerial vehicle j epsilon phi for unloading the task is shown as (11):

the transmission energy from the ground terminal equipment i e psi to the unmanned aerial vehicle j e phi for unloading the task is shown as (12):

s1-2-2 calculation model

Task _i The time to unload to drone j e phi execution is shown as (13):

wherein

Task _i The computational energy consumption offloaded to drone j e phi execution is shown in (14):

wherein mu _c Representing the effective capacitance coefficient of the drone.

S1-3 problem description

S.t.

Representing the CPU frequency allocation of the drone,

the decision to offload a task is made,

indicating the position and elevation of the drone,

representing the transmission power of the ground terminal equipment.

Step 2, solving the unloading decision of the task, the optimal position and elevation angle of the unmanned aerial vehicle and the transmission power of the ground terminal equipment based on a differential evolution algorithm and a greedy algorithm, and the steps are as follows:

s2-1, constructing a mathematical model under the condition that the CPU of the unmanned aerial vehicle is assigned to each task to calculate the frequency F. And under the condition that the CPU calculation frequency F distributed to each task by the unmanned aerial vehicle is given, the unloading decision of the task, the optimal position and the elevation angle of the unmanned aerial vehicle and the transmission power of the ground terminal equipment are optimized, and a differential evolution algorithm and a greedy algorithm are adopted for solving. The solution target is consistent with the problem P1, and the number of the bearing tasks of the unmanned aerial vehicle is maximized. The mathematical model P2 of the optimization problem can be written as follows:

S.t.

Are the optimization variables.

the problem P2 is solved, given the CPU calculation frequency F assigned to each task by the drone,firstly, solving the position and the elevation angle Q of the unmanned aerial vehicle based on a differential evolution algorithm, solving the transmission power P of ground terminal equipment and the unloading decision A of tasks based on a greedy algorithm, and finally obtaining the maximum bearing task number of the unmanned aerial vehicle

Setting maximum iteration times tau of differential evolution algorithm _max =10000, and let the current iteration number τ =1.

i) The population is initialized as follows:

a coding mechanism is proposed in which a population set represents

Wherein

Represents the set of the position and elevation of the Tth iteration unmanned aerial vehicle, Q _j (τ)＝(X _j (τ)，Y _j (τ)，H _j (τ)，θ _j (τ)) represents the position and elevation coding for drone j ∈ φ, while noting Q _j (τ)＝q _j (X _j (τ)，Y _j (τ)，H _j (τ)，θ _j (τ)) represents the position and elevation angle of the drone j e Φ at the τ th iteration, and the value range is as follows:

wherein c is ₁ And 0 each represents X _j Upper and lower bounds of c ₁ Representing a constant in meters (m). c. C ₂ And 0 each represents Y _j Upper and lower bounds of c ₂ Denotes a constant with units of meter (m), H _max And H _min Each represents H _j Upper and lower bounds in meters (m), θ _max And theta _min Respectively represent theta _j An upper bound and a lower bound.

For convenience of description X _j (τ)，Y _j (τ)，H _j (τ)，θ _j (τ) value range, let us assume

(17a) - (17 d) can be collectively expressed as follows:

for example when

In formula (18)

Randomly generating decision variablesX _j (τ)，Y _j (τ)，H _j (τ)，θ _j The initial population of (τ) is calculated as follows:

wherein rand (0, 1) denotes a random selection of a constant from 0-1.

For example when

Time, randomly generate

(1) let j =1,j denote the serial number of the drone, and randomly generate the position and elevation Q of drone j based on equation (20) _j (τ)＝(X _j (τ)，Y _j (τ)，H _j (τ)，θ _j (τ)), and Q is added _j (τ) put into the set of positions and elevations Q (τ) of drones for the τ -th iteration.

(3) Randomly generating position and elevation angle Q of unmanned aerial vehicle j +1 _j+1 (τ), iota = iota +1. Judging whether the position of each unmanned aerial vehicle in the unmanned aerial vehicle j +1 and the unmanned aerial vehicle position and elevation angle set Q (tau) of the tau iteration meets constraint expressions (16 g) and (16 j), namely Q (tau) and Q _j+1 Whether or not the position of (τ) satisfies the constraint expressions (16 g) and (16 j). The judgment and selection are as follows:

if Q (τ) and Q _j+1 (τ) satisfies the constraint equations (16 g) and (16 j), which indicates Q (τ) and Q _j+1 (τ) distance between drones is greater than or equal to the nearest distance limit

That is, no collision occurs between drones in drones j +1 and Q (τ), and the coverage of drones in drones j +1 and Q (τ) is disjoint, then let j = j +1, and Q is assigned _j (tau) putting the unmanned aerial vehicle position and elevation angle set Q (tau), and skipping to the step (4). If Q (τ) and Q _j+1 (τ) does not satisfy constraint equation (16 f) and equation (16 j), indicating that the generation of the j +1 st drone position was unsuccessful. Iota is less than or equal to _max And (4) if the answer is positive, skipping to the step (3) if the answer is positive, otherwise skipping to the step (1).

(4) And (3) judging whether j is less than or equal to N, and if yes, returning to the step (2). Otherwise, the positions and the elevation angles of all the unmanned planes are successfully generated, and the initial population Q (tau) of the unmanned planes is obtained.

ii) calculating the transmission power of the ground terminal equipment according to the new position and the elevation angle of the unmanned aerial vehicle, and the steps are as follows:

and according to the position and the elevation angle of the unmanned aerial vehicle j e phi and the position information of the user i e phi, the coverage range of which unmanned aerial vehicle the ground terminal equipment i belongs to is obtained through the formula (16 f). Calculating the frequency F and the maximum time delay T of the CPU assigned to a task for a given drone according to equation (16 b) _max And obtaining the transmission rate required by the ground terminal equipment i epsilon psi to the unmanned aerial vehicle, wherein the transmission rate meets the following constraint:

Wherein the first type task psi ₁ Having the highest priority, ground terminal equipment i epsilon psi ₁ Indicating that it is not within the coverage of the drone, at which time Task _i Can only be done locally, in which case the unloading decision a for the τ th iteration _i，j (τ)＝0。

Task psi of the second type ₂ At this time, the ground terminal equipment i is epsilon psi ₂ In the coverage of unmanned aerial vehicle, task _i Can be unloaded to an unmanned aerial vehicle for execution, and the tau-th iteration ground terminal equipment i epsilon psi can be calculated based on the transmission power obtained in the step ii) ₂ Transmission rate r to drone j _i，j (τ) is calculated. Unmanned aerial vehicle assignment to Task _i Under the condition that the calculation resources satisfy the formulas (16 b) and (16 c), the unloading decision is solved based on a greedy algorithm, and the selection strategy of the greedy algorithm is that the ground terminal equipment i belongs to psi ₂ Transmission rate r to drone j _i，j (τ), i.e. transmission rate r _i，j (τ) fastest is selected first, with the unload decision a of the τ th iteration _i，j (τ)＝1。

Task type III ₃ That is, after the unmanned aerial vehicle computing resources are fully loaded, the tasks can only be performed locally, namely, the total task psi is except psi ₁ 、ψ ₂ Task outside, unload decision a for the τ th iteration at this time _i，j (τ)＝0。

iv) calculating a target value

Obtaining j e phi position and elevation angle of the unmanned aerial vehicle of the tau iteration based on the steps ii) and iii)

The transmission power of the ground terminal equipment and the task unloading decision can obtain the result { P (tau), Q (tau) of the tau iterationAnd A (tau), wherein P (tau) represents the transmission power of the ground terminal equipment at the tau iteration, Q (tau) represents the unmanned aerial vehicle position set at the tau iteration, and A (tau) represents the task unloading decision at the tau iteration. Calculating a target value of the tau iteration based on the result of the tau iteration, namely the maximum number of bearing tasks of the unmanned aerial vehicle

mutation operation: according to

Is provided with

For the unmanned plane j epsilon phi position and elevation angle obtained after the tau iteration variation,

respectively correspond to

By mutation operations of

The calculation formula of (a) is as follows:

equation (23) represents drone j for the τ th iterationEpsilon phi position and elevation angle q _j (X _j (τ)，Y _j (τ)，H _j (τ)，θ _j (τ)) performing a mutation operation, wherein j ₁ 、j ₂ 、j ₃ E phi represents that 3 unmanned aerial vehicles with different numbers are randomly selected from the unmanned aerial vehicles, and tau represents Q in a differential evolution algorithm _j F denotes the scaling factor, taking F =0.9.

And (3) cross operation: is also provided with

Selected by cross probability

Wherein

The calculation formula of (c) is as follows:

equation (24) represents that the position of the drone j ∈ phi at the τ -th iteration is crossed with the elevation angle, CR represents the cross probability, and CR =0.9.

Through mutation and crossing to obtain

vi) the selection operation is as follows:

the selection is based on a greedy idea, i.e. the largest of the target values is selected as the new individual. Crossing the variation to obtain a population U (tau) = { U = [ (U) ] ₁ (τ)、U ₂ (τ)、…U _j (τ)、…U _N (τ) } is compared with the original population Q (τ) = { Q = ₁ (τ)、Q ₂ (τ)、…Q _j (τ)、…Q _N (τ) }, the comparison formula is shown in equation (25):

comparison L ^* (τ) and L (τ), as follows:

vii) judgment of τ +1 > τ _max And if yes, stopping loop iteration, and outputting { P (tau + 1), Q (tau + 1) and A (tau + 1) }, otherwise, tau = tau +1, and jumping to the step v).

Step 3, according to the position and the elevation angle Q of the unmanned aerial vehicle obtained in the step 2 and the transmission power P of the ground terminal equipment, solving a final unloading decision A of the unmanned aerial vehicle and a Task allocated to the unmanned aerial vehicle _i The CPU calculates the frequency F, and the solving steps are as follows:

S.t.

wherein x ₁ = (A, F), wherein

The following equations (8), (9), (11) and (12) show

Are all known values, i.e., are constants.

And S3-2, after the position and the elevation angle Q of the unmanned aerial vehicle and the transmission power P of the ground terminal equipment are obtained according to the step 2, an unloading decision A of the task and a computing resource allocation F of the unmanned aerial vehicle are solved by adopting a convex optimization method.

The specific operation of S3-2-1 non-convex-to-convex is as follows:

i) Order to

And with

Respectively representing the expressions (26 b) and (26 c), and obtaining the Hessian of (26 b) and (26 c)Matrix, as follows:

the equation (26 b) is first linearized, and in order to avoid the denominator being zero, a small variable epsilon is introduced ₁ Equation (26 b) can be restated as:

substituting formula (29) into formula (28) to give formula (30):

substituting formula (29) into formula (26 e) to give formula (31):

Also, because of the formula (29), can obtain

And replace

In (1)

The formula (32) can be obtained finally:

then model P3 may be rewritten to model P4 as follows:

S.t.

for formula (34), define

From equations (32) and (34), the constraint factor product ω can be obtained _i，j ：

By using

Substitution of equation (35) yields equation (36) as follows:

definition of

Because of the fact that

Therefore, it is possible to

Then σ can be obtained _i，j The range of (c) is as follows:

definition of

From equations (34) and (37), the constraint factor product can be obtained

By using

Substitution of equation (38), yields equation (39), shown below:

model P4 can be transformed into P5 as follows:

S.t.

(38)，(39) (40g)

wherein

Because of

Therefore, it is possible to

The trend of (1) is the same, so the target formula is changed to

A mathematical model P6 was obtained as follows:

S.t.(40b)，(40c)，(40d)，(40e)，(40f)，(40g) (41b)

s3-2-2: adopting KKT conditions to solve the unloading decision of the unmanned aerial vehicle and the calculation frequency of the task, and specifically comprising the following steps:

i) Solving problem P6, constructing Lagrangian function and dual problem of P6, and ordering

lagrange multipliers of expressions (40 b) - (40 c),

the Lagrangian multiplier of expression (40 d),

the Lagrangian multiplier of expression (40 e),

a Lagrangian multiplier of expression (40 f),

each of the Lagrange multipliers represented by the formula (40 g),

respectively, a Lagrange multiplier of formula (40 j), then

The lagrangian function of problem P6 is as follows:

the dual function of the mathematical model P6 is defined as

The dual problem is that

s.t.λ≥0；

ii) Lagrangian function (42) for each pair

Calculating a partial derivative, wherein the steps are as follows:

lagrange function (42) pairs

The partial derivatives are calculated as follows:

lagrange function (42) pair

The partial derivatives are calculated as follows:

lagrange function (42) pairs

The partial derivatives are calculated as follows:

lagrange function (42) pair

The partial derivatives are calculated as follows:

lagrange function (42) pair

The partial derivatives are calculated as follows:

lagrange function (42) pair

The partial derivatives are calculated as follows:

iii) The conditions according to KKT are as follows:

from equation (43), equation (50) can be derived, as follows:

formula (51) is obtainable from formula (44):

formula (52) is obtained according to formula (45):

equations (53) and (54) are obtained from equations (46) and (47):

finding gamma in the formula (36) _i，j 、ω _i，j While the related equation can be found:

therefore, it can be analyzed from the formulas (55) and (56) that (53) and (54) are γ, respectively _i，j Upper and lower bounds of (a), if γ _i，j When the value between (52) and (53) does not take the boundary, then

And

are both 0.

Equations (57) and (58) are obtained from equations (48) and (49):

the same can be found in equation (39) _i，j 、

While the related equation can be found:

therefore, according to the equations (59) and (60), the values of σ of (57) and (58), respectively, can be analyzed _i，j Upper and lower bound of (a), if _i，j If the value between (57) and (58) does not take the boundary, then

And with

Are both 0.

By analyzing (40 d), (40 e), (40 f) and (40 g), the results were obtained

Since the portion is not 0, according to the KKT condition,

are both 0. While not taking sigma _i，j And gamma _i，j The boundary of (1) is then

Both are 0, initialization is performed so that i =1.

Equation (50) can be simplified to (61):

iv) initialization

At this time

The cases of (c) are as follows:

calculating Lagrange function according to equations (44) and (45)

The value of (c).

As follows:

ix) calculation task unmanned j assignmentTask _i The calculation frequency of (c):

by passing

Can find gamma _i，j The formula is as follows:

The formula is as follows:

x) by A ₁ The unload decision a is obtained as follows:

wherein A (a) _i，j ) Representing a in the offload decision set A _i，j ，A ₁ (a _i，j ) Representing offload decision set A ₁ A in (a) _i，j 。

S3-2-3 by

ii) pair

And (4) judging, wherein the judging step is as follows:

a if

The steps are as follows:

(1) selection A ₁ 0 < A in ₁ (a _i，j ) The value in the interval < 0.5, and secondly recording a in this interval _i，j Task corresponding to the minimum value of

Is recorded as i ₁ . Let A (a) _i，j )＝1，A ₁ (a _i，j ) And =0. Is re-paired by the formula (51)

And (6) performing operation.

(2) If it is

Then

(3) If it is

b is if

The steps are as follows:

first, A is selected ₁ A in 0.5. Ltoreq ₁ (a _i，j ) The value in the interval of ≦ 1, and then recording a in this interval _i，j Task of maximum value of

Is marked as i ₂ 。

Order to

Is newly paired by the formula (51)

Carry out the operation if

Then

If it is

And returning to the step i) again.

iv) calculating

Step 4 compares O (δ) with O (δ + 1), if O (δ 0+ 1) > O (δ 1), O (δ + 1) = O (δ + 1), and records F, a, Q, P for O (δ + 1), otherwise O (δ + 1) = O (δ), keeping F, a, Q, P for O (δ). Judging that delta +1 is larger than delta _max And if not, making delta = delta +1, skipping to the step 2 for a new iteration based on the calculated F, and if so, ending the iteration to obtain F, A, Q and P of the optimized variables and the maximum bearing task number O (delta) of the unmanned aerial vehicle.